Abstract and Applied Analysis

A Two-Grid Method for Finite Element Solutions of Nonlinear Parabolic Equations

Chuanjun Chen and Wei Liu

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Abstract

A two-grid method is presented and discussed for a finite element approximation to a nonlinear parabolic equation in two space dimensions. Piecewise linear trial functions are used. In this two-grid scheme, the full nonlinear problem is solved only on a coarse grid with grid size H . The nonlinearities are expanded about the coarse grid solution on a fine gird of size h , and the resulting linear system is solved on the fine grid. A priori error estimates are derived with the H 1 -norm O ( h + H 2 ) which shows that the two-grid method achieves asymptotically optimal approximation as long as the mesh sizes satisfy h = O ( H 2 ) . An example is also given to illustrate the theoretical results.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 391918, 11 pages.

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365168880

Digital Object Identifier
doi:10.1155/2012/391918

Mathematical Reviews number (MathSciNet)
MR2975310

Zentralblatt MATH identifier
1253.65159

Citation

Chen, Chuanjun; Liu, Wei. A Two-Grid Method for Finite Element Solutions of Nonlinear Parabolic Equations. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 391918, 11 pages. doi:10.1155/2012/391918. https://projecteuclid.org/euclid.aaa/1365168880


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